# Arithmetic

This section includes several notations that incorporate the Additive and Multiplicative Principles of Iconic Arithmetic. The image shows a Numerical Pocket Piece from 1753. It shows the Table for Multiplication and Division (a modern times table) from 3 to 9 and is inscribed as “a new and short method.” The times table for 2 is not included because doubling was taught as a necessary math skill, and was included in the algorithm for achieving multiplication and division.

## Section Contents

Iconic arithmetic defines addition and multiplication as physical activities.

Unit-ensembles are collections of identical sticks, pebbles, marks, tokens, or fingers.

Depth-value notation provides a convenient and simple way to group larger collections of units.

Container numbers illustrate unit-ensembles and depth-value working in concert.

Parens notation permits containers to be expressed by a string of typographical characters.

Network numbers express iconic arithmetic as composable networks.

Block numbers express iconic arithmetic as physical constructions using blocks.

Spencer-Brown numbers have units that act both as numbers and as operations.